iOS 7 Apps on iPad show up as installed but are not actually installed

I have a few apps that appear to be installed on my iPad running iOS 7 but are not actually installed.

For instance, the app is no where on any home screen or inside any folder, but visiting the App Store and navigating to the app page on my iPad does not show an iCloud download button or a "Free/Buy" button.

The OS seems to think the app is there, but it's not. If it is installed I have no way of seeing or using it.

Things I've already tried:

• Uninstalling, re-installing through iTunes (latest version)
• Signing out of the iTunes/App Store on my iPad and signing back in

Has anybody had this problem or is there a fix anyone knows about?

Update (screenshots)

If they are installed, then the App Store should now say OPEN instead of buy, or re-download etc.

You can try to find the apps with Spotlight to see if they are just hidden icons (various bugs can hide your apps on occasion) or genuinely not installed; just swipe down from the center of the screen and search for the apps name. if it finds it, then:

Settings > General > Reset > Reset Home Screen will bring back all your missing icons, at the expense of removing all your folders and putting the pre-installed apps back to their original positions.

I had this problem, too. It turned out the apps I was trying to install were a higher rating than I had set in my settings (12+ when I had set 4+). Once I increased the rating limit in my settings the apps installed just fine.